Question: Add the following rational expressions. $\dfrac{25}{7m^2+9}+\dfrac{14m-11}{7m^2+9}=$
Answer: We want to add two rational expressions whose denominators are equal. We can do this by adding the numerators and keeping the denominator the same. [Does this fit with how we add rational numbers?] $\begin{aligned} &\phantom{=}\dfrac{25}{7m^2+9}+\dfrac{14m-11}{7m^2+9} \\\\ &=\dfrac{(25)+(14m-11)}{7m^2+9} \\\\ &=\dfrac{25+14m-11}{7m^2+9} \\\\ &=\dfrac{14m+14}{7m^2+9} \end{aligned}$ In conclusion, $\dfrac{25}{7m^2+9}+\dfrac{14m-11}{7m^2+9}=\dfrac{14m+14}{7m^2+9}$